$2\mathrm{.}10$ A Rankine cycle operates with inlet steam at $75$ bar and $\backslash (320^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ condensing at $\backslash (50^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ and generates $250$ MW of power. The cycle features a single stage of reheat that returns the steam to $\backslash (320^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ A closedtype feedwater heater receives bled steam at the reheat pressure and cascades the drains back to the condenser. The high$-$pressure turbine has a polytropic efficiency of $\backslash (91\backslash \%\backslash ),$ while the low$-$pressure turbine operates at $\backslash (93\backslash \%\backslash )$ efficiency. The pump operates isentropically$.$ Calculate $($a$)$ the mass flow rate of the steam at the turbine inlet in kilogram per second. $($b$)$ the cycle efficiency, $($c$)$ the cycle work ratio. Use $\backslash (\backslash$mathrm$\{$TTD$\}=-2\mathrm{.}5^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$